Fiona bought some socks that cost $[tex]$4.95$[/tex] for each pair and some belts that cost $[tex]$6.55$[/tex] each. Fiona spent $[tex]$27.95$[/tex] in all. Let [tex]$a$[/tex] represent the number of pairs of socks purchased and [tex]$b$[/tex] the number of belts purchased.

Which equation models the situation?

A. [tex]$a+b=11.50$[/tex]
B. [tex]$a+b=27.95$[/tex]
C. [tex]$4.95 a+6.55 b=27.95$[/tex]
D. [tex]$6.55 a+4.95 b=27.95$[/tex]

Question

Fiona bought some socks that cost $[tex]$4.95$[/tex] for each pair and some belts that cost $[tex]$6.55$[/tex] each. Fiona spent $[tex]$27.95$[/tex] in all. Let [tex]$a$[/tex] represent the number of pairs of socks purchased and [tex]$b$[/tex] the number of belts purchased. 
 
Which equation models the situation? 
 
A. [tex]$a+b=11.50$[/tex] 
B. [tex]$a+b=27.95$[/tex] 
C. [tex]$4.95 a+6.55 b=27.95$[/tex] 
D. [tex]$6.55 a+4.95 b=27.95$[/tex]

GinnyAnswer · Answer

The total cost of socks is 4.95 a . 
 The total cost of belts is 6.55 b . 
 The sum of the cost of socks and belts equals the total amount spent: 4.95 a + 6.55 b = 27.95 . 
 The equation that models the situation is 4.95 a + 6.55 b = 27.95 ​ . 
 
 Explanation 
 
 Analyze the problem Let's analyze the given information to form an equation that models the situation. We know the cost of each pair of socks, the cost of each belt, the total amount Fiona spent, and the variables representing the number of pairs of socks and belts purchased. 
 
 Calculate the cost of socks The cost of each pair of socks is $4.95 , and a represents the number of pairs of socks purchased. Therefore, the total cost of the socks is 4.95 a . 
 
 Calculate the cost of belts The cost of each belt is $6.55 , and b represents the number of belts purchased. Therefore, the total cost of the belts is 6.55 b . 
 
 Form the equation Fiona spent a total of $27.95 . This amount is the sum of the total cost of the socks and the total cost of the belts. So, we can write the equation as: 4.95 a + 6.55 b = 27.95 
 
 State the final answer The equation that models the situation is 4.95 a + 6.55 b = 27.95 .

Examples 
 Imagine you are at a store buying apples and bananas. Each apple costs $0.75 and each banana costs $0.50 . You have a total of $5.00 to spend. If x represents the number of apples and y represents the number of bananas, the equation 0.75 x + 0.50 y = 5.00 models the situation. This type of equation helps you determine how many apples and bananas you can buy without exceeding your budget. Understanding how to create and solve these equations is useful for budgeting and making purchasing decisions in everyday life.

Answer (1)

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